Poor Hero takes quite a hit when it comes to her honor and reputation. Claudio is quick to believe the worst of her, as in this scene (4.1) where he angrily dismisses her:

Out on thee! Seeming! I will write against it: You seem to me as Dian in her orb, As chaste as is the bud ere it be blown; But you are more intemperate in your blood Than Venus, or those pamper'd animals That rage in savage sensuality."

Of course, Beatrice continually fights for her honor, not in the same way as Hero; she is much more concerned about being perceived as an equal. She has an uphill battle with Benedick, who in Act 1.1 has the following to say about women:

That a woman conceived me, I thank her; that she brought me up, I likewise give her most humble thanks: but that I will have a recheat winded in my forehead, or hang my bugle in an invisible baldrick, all women shall pardon me.